The Research Of Small Damping Ratio Diagnosis Based On The Inner Product Correlation

In engineering,the damping ratio is a measure of describing how oscillations in a system die down after a disturbance.It is important to identify the damping ratio in the structure of fault diagnosis,safety assessment,real-time monitoring of vibration,load identification,etc. Structural vibration responses are a function of damping ratio,which directly affects the reliability of the results of the structure dynamic response analysis.The damping ratio is loss capacity of system energy,which plays an important role in the control of vibration,shock and noise.Frequency, damping ratio and amplitude are three elements of vibration;the damping ratio is the most difficult one to be measured.Therefore,improving the damping(or damping ratio) accuracy is an important research work.A method for damping estimation based on the inner product correlation is presented,which aims at avoiding the effect of the datum truncation errors.There are two main steps for this method.First,the resonance frequency of a response signal is calculated by using Fourier Transform and the Non-Prior base signal transform method.Then choose a decaying exponential function and normalize it.After that,the Cauchy-Schwartz inequality is carried out and an optimization method is adopted to search the maximum of the inner product module,meanwhile, the damping ratio is estimated.This method applies both to single degree of freedom and multi degree of freedom system.The damping ratio could be computed directly by a response signal,which solve the datum truncation errors of traditional problem.Without increasing the sampling length,the small damping ratio accuracy has been greatly improved.Simulation result shows that this method is not be influenced by noise which has high precision in small damping ratio identification.The application of this method to measure damping ratios on a cantilever beam is described.This method lays the foundation for the further research of damping ratio diagonosis.